Question

Angles ∠2 and ∠4 are vertical angles. If the m/∠2 = 3x and the m/∠4 = 120, what is the value of x?

a) 20
b) 40
c) 60
d) 80

Answer 1

By setting the equations of the congruent vertical angles equal to each other (3x = 120), we can solve for x and find that x equals 40.

Step-by-step explanation:

If ∠2 and ∠4 are vertical angles, and the measure of ∠2 is given as 3x degrees and the measure of ∠4 is given as 120 degrees, then we can find the value of x by setting these measures equal to each other since vertical angles are congruent.

The equation is: 3x = 120.

To solve for x, you would divide both sides of the equation by 3.

x = 40

Therefore, the value of x is 40, which corresponds to answer choice (b).